Problem: Solve for $x$ : $3x^2 + 24x - 27 = 0$
Solution: Dividing both sides by $3$ gives: $ x^2 + {8}x {-9} = 0 $ The coefficient on the $x$ term is $8$ and the constant term is $-9$ , so we need to find two numbers that add up to $8$ and multiply to $-9$ The two numbers $-1$ and $9$ satisfy both conditions: $ {-1} + {9} = {8} $ $ {-1} \times {9} = {-9} $ $(x {-1}) (x + {9}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -1) (x + 9) = 0$ $x - 1 = 0$ or $x + 9 = 0$ Thus, $x = 1$ and $x = -9$ are the solutions.